Spheres In Newtonian Fluids Research Articles

Four-dimensional flow field near a sphere settling in Newtonian fluid

This paper presents time-resolved, three-dimensional measurements coupling particle trajectories with flow fields around settling spheres in Newtonian fluids. The experiments cover a range of particle Reynolds numbers (Re), spanning from 1.6 to 6. Our calculated drag coefficients, derived from sphere trajectories, closely align with values reported in the literature. Notably, our high spatial resolution reveals oscillations, potentially corresponding to the “streamwise oscillations” phenomenon discussed by Horowitz and Williamson [“The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres,” J. Fluid Mech. 651, 251 (2010)]. For a single sphere, we extract the three-dimensional flow field using particle tracking velocimetry. Discrete particle tracks are meticulously interpolated onto a regular grid using a fine-scale reconstruction based on the vortex-in-cell method. Leveraging the known sphere position, we introduce a sphere-centered coordinate system, enabling time-averaging of flow properties. Additionally, we interpolate and analyze the pressure field on the sphere's surface, employing proper orthogonal decomposition to unveil distinct pressure fluctuation modes.

Stokes flow of Micropolar fluid beyond fluid sphere with slip condition

AbstractThe present study is about the impact of the fluid motions of the micropolar fluids internally and externally of the fluid sphere with an interfacial slip condition using the analytic method. This enables to bring out solutions for the flow fields as indicated by the stream functions and the drag of the sphere. The work explores the possibilities of change in the slip and drag conditions and their evaluations are graphically proven. Apart from this, the study also identifies that the micropolar fluid flows beyond the Newtonian fluid sphere and vice versa by analyzing the stream functions and the drag of the sphere.

Modeling the Settling Velocity of a Sphere in Newtonian and Non-Newtonian Fluids with Machine-Learning Algorithms

The traditional procedure of predicting the settling velocity of a spherical particle is inconvenient as it involves iterations, complex correlations, and an unpredictable degree of uncertainty. The limitations can be addressed efficiently with artificial intelligence-based machine-learning algorithms (MLAs). The limited number of isolated studies conducted to date were constricted to specific fluid rheology, a particular MLA, and insufficient data. In the current study, the generalized application of ML was comprehensively investigated for Newtonian and three varieties of non-Newtonian fluids such as Power-law, Bingham, and Herschel Bulkley. A diverse set of nine MLAs were trained and tested using a large dataset of 967 samples. The ranges of generalized particle Reynolds number (ReG) and drag coefficient (CD) for the dataset were 10−3 < ReG (-) < 104 and 10−1 < CD (-) < 105, respectively. The performances of the models were statistically evaluated using an evaluation metric of the coefficient-of-determination (R2), root-mean-square-error (RMSE), mean-squared-error (MSE), and mean-absolute-error (MAE). The support vector regression with polynomial kernel demonstrated the optimum performance with R2 = 0.92, RMSE = 0.066, MSE = 0.0044, and MAE = 0.044. Its generalization capability was validated using the ten-fold-cross-validation technique, leave-one-feature-out experiment, and leave-one-data-set-out validation. The outcome of the current investigation was a generalized approach to modeling the settling velocity.

MHD fluid flow with the effect of mixed convection passing on a magnetic sphere in newtonian nano fluid

This paper considers magneto-hydrodynamics (MHD) fluid flow with the effect of mixed convection passing on a magnetic sphere in nano fluid. Titanium dioxide (TiO2) is chosen as solid particle in nano fluid. The dimensional governing equations are developed from continuity equation, momentum equation, and energy equation. Furthermore, the dimensional governing equations are transformed into the non-dimensional governing equation by using non-dimensional parameters and variables. Then, the non-dimensional governing equations are transformed into similarity equations using stream function and then solved numerically using implicit finite difference method. The results of numerical solution are obtained using variation of non-dimensional parameters which consist of magnetic parameter, mixed convective parameter, and volume fraction. The numerical results show that the velocity and temperature decrease when magnetic parameter increases. The velocity and temperature increase when mixed convective parameter also increases. Finally, the velocity decreases and temperature increases when volume fraction parameters increase.

Shear thickening in concentrated suspensions of smooth spheres in Newtonian suspending fluids.

Shear thickening is a phenomenon in which the viscosity of a suspension increases with increasing stress or shear rate, sometimes in a discontinuous fashion. While the phenomenon, when observed in suspensions of corn starch in water, or Oobleck, is popular as a science experiment for children, shear thickening is actually of considerable importance for technological applications and exhibited by far simpler systems. Concentrated suspensions of smooth hard spheres will exhibit shear thickening, and understanding this behavior has required a fundamental change in the paradigm of describing low-Reynolds-number solid-fluid flows, in which contact forces have traditionally been absent. Here, we provide an overview of our understanding of shear thickening and the methods that have been developed to describe it, as well as outstanding questions.

Effects of Uniform Heat Flux and Velocity-Slip Conditions at Interface on Heat Transfer Phenomena of Smooth Spheres in Newtonian Fluids

The effects of the uniform heat flux and a linear velocity-slip on the heat transfer phenomena of spheres in Newtonian fluids are numerically investigated using semi-implicit marker and cell (SMAC) method implemented on a staggered grid arrangement in spherical coordinates. The solver is thoroughly benchmarked through domain independence, grid independence, and comparison with literature. Further extensive results are obtained in the range of conditions as: Reynolds number, Re = 0.1–200; Prandtl number, Pr = 1–100; and dimensionless slip number, λ = 0.01–100. The results are presented and discussed such that the isotherm contours and the local and average Nusselt numbers of isoflux spheres with velocity-slip at the interface are compared with their isothermal spheres counterparts under identical conditions. Briefly, the results indicate that the average Nusselt numbers of isoflux spheres are large compared to those of isothermal spheres under identical conditions. Finally, an empirical correlation is developed for the average Nusselt numbers of the spheres in Newtonian fluids with velocity-slip and the uniform heat flux conditions along the fluid–solid sphere interface.

White Dwarf Stars as Polytropic Gas Spheres

Due to the highly degeneracy of electrons in white dwarf stars, we expect that the relativistic effects play very important role in these stars. In the present article, we study the properties of the condensed matter in white dwarfs using Newtonian and relativistic polytropic fluid sphere. Two polytropic indices (namely n=3 and n=1.5) are proposed to investigate the physical characteristics of the models. We solve the Lane-Emden equations numerically.. The results show that the relativistic effect is small in white dwarf stars.

Heat Transfer Phenomena of Assemblages of Smooth Slip Spheres in Newtonian Fluids

Combined effects of slip velocity and volume fraction of slip spheres on the heat transfer characteristics of multiple slip spheres are numerically investigated within the framework of a free surface cell model combined with a linear slip velocity along the surface of the slip spheres. The governing conservation equations of the mass, momentum, and energy are solved by a segregated approach using a simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The convection and diffusion terms of conservation equations are discretized using quadratic upstream interpolation for convective kinematics and second‐order central differencing schemes, respectively. Prior to obtaining new results, this numerical solver is validated by comparison of present results with the existing literature values. Further new results are obtained for a range of conditions as; Reynolds number, Re: 0.1–200; Prandtl number, Pr: 1–100; volume fraction of slip spheres, Φ: 0.1–0.5 and slip parameter, λ: 0.01–100. The effects of these dimensionless parameters on isotherm contours and local and average Nusselt numbers are thoroughly delineated. Finally, a new empirical correlation for the average Nusselt number of multiple smooth slip spheres is proposed on the basis of present numerical results.

A note on the breathing mode of an elastic sphere in Newtonian and complex fluids

Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [Pelton et al., “Viscoelastic flows in simple liquids generated by vibrating nanostructures,” Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. We also comment on the effect of fluid viscoelasticity on the idea of destroying virus particles by acoustic resonance.

Rheology of Non-Brownian Suspensions

Suspensions of non-Brownian particles are commonly encountered in applications in a large number of industries. These suspensions exhibit nonlinear flow behavior, even in Newtonian suspending fluids under conditions where inertial effects can be ignored and linearity would normally be expected. We review the observed rheological behavior, emphasizing concentrated suspensions of spheres in Newtonian fluids, and we examine both particle-level and continuum approaches to describing the nonlinear behavior. Particle-particle nonhydrodynamic interactions appear to be important in concentrated suspensions. Continuum descriptions are not yet adequate to describe the observed behavior.

Coarse-Grained Modeling of the Titration and Conductance Behavior of Aqueous Fullerene Hexa Malonic Acid (FHMA) Solutions

The coarse-grained continuum primitive model is developed and used to characterize the titration and electrical conductance behavior of aqueous solutions of fullerene hexa malonic acid (FHMA). The spherical FHMA molecule, a highly charged electrolyte with an absolute valence charge as large as 12, is modeled as a dielectric sphere in Newtonian fluid, and electrostatics are treated numerically at the level of the non-linear Poisson-Boltzmann equation. Transport properties (electrophoretic mobilities and conductances) of the various charge states of FHMA are numerically computed using established numerical algorithms. For reasonable choices of the model parameters, good agreement between experiment (published literature) and modeling is achieved. In order to accomplish this, however, a moderate degree of specific binding of principal counterion and FHMA must be included in the modeling. It should be emphasized, however, that alternative explanations are possible. This comparison is made at 25 °C for both Na(+) and Ca(2+) principal counterions. The model is also used to characterize the different charge states and degree of counterion binding to those charge states as a function of pH.

Influence of Interlayer Exchanges on Vorticity-Aligned Colloidal String Assembly in a Simple Shear Flow

Hard spheres in Newtonian fluids serve as paradigms for Non-Newtonian materials phenomena exhibited by colloidal suspensions. A recent experimental study (Cheng et al. 2011 Science, 333, 1276) showed that upon application of shear to such a system, the particles form string-like structures aligned in the vorticity direction. We explore the mechanism underlying this out-of-equilibrium organization with Steered Transition Path Sampling, which allows us to bias the Brownian contribution to rotations of close pairs of particles and alter the dynamics of the suspension in a controlled fashion. Our results show a strong correlation between the string structures and the rotation dynamics. Specifically, the simulations show that accelerating the rotations of close pairs of particles, not increasing their frequency, favors formation of the strings. This insight delineates the roles of hydrodynamics, Brownian motion, and particle packing, and, in turn, informs design strategies for controlling the assembly of large-scale particle structures.

Wall Retardation Effects on Flow and Drag Phenomena of Confined Spherical Particles in Shear-Thickening Fluids

In this work, effects of the wall retardation, Reynolds number, and shear-thickening viscosity behavior of fluids on flow and drag phenomena of confined spherical particles are presented. The governing mass and momentum conservation equations are solved using computational fluid dynamics-based commercial software. The numerical solver is thoroughly validated by comparing present results with existing literature for the case of unconfined spheres in Newtonian and shear-thickening fluids. Extensive new results were presented in the following range of conditions: Reynolds number, Re, 1–100; wall factor, λ, 2–5; and power-law index, n, 1–1.8. The wall factor (λ) is defined as the ratio between the tube diameter and the particle diameter. The severity of wall retardation effects increases with increasing power-law index. For fixed values of the Reynolds number, the recirculation wake length decreases with decreasing wall factor and/or increasing power-law index. For n = 1.8, the wall retardation effects are ve...

Unsteady conjugate forced convection heat/mass transfer in ensembles of Newtonian fluid spheres

The unsteady, conjugate, forced convection heat/mass transfer from ensembles of mono-size Newtonian fluid spheres to Newtonian fluids has been studied at moderate Peclet and Reynolds numbers. The cell model has been used to account for the spheres hydrodynamic interactions. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere exterior Reynolds number are Re 2 ⩽ 200 . The influence of the voidage and physical properties ratios on the heat/mass transfer rate was analysed for sphere Peclet numbers, Pe 1(2) ⩽ 10 4, and three fluid – fluid systems: gas–liquid, liquid–liquid and liquid–gas.

Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes

This work presents nonsimilar boundary layer solutions for double-diffusion natural convection near a sphere with constant wall heat and mass fluxes in a micropolar fluid. A coordinate transformation is employed to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. Higher vortex viscosity tends to retard the flow, and thus decreases the local convection heat and mass transfer coefficients, raising the wall temperature and concentration. Moreover, the local convection heat and mass transfer coefficients near a sphere in Newtonian fluids are higher than those in micropolar fluids.

Anomalous bulk viscosity of polymer-nanocomposite melts

Nanoparticles dispersed in polymer melts have recently been shown to decrease the bulk viscosity. This contradicts expectations based on Einstein's well-known theory for effective viscosity of dilute, random dispersions of rigid spheres in Newtonian fluids. In this paper, we examine a continuum hydrodynamic model where a layer of polymer at the nanoparticle–polymer interface has a different viscosity and density than the bulk polymer. When the layer thickness is greater than the nanoparticle radius, and the layer viscosity is lower than that of the bulk polymer, the intrinsic viscosity is comparable to the unexpectedly large, negative values reported experimentally by Mackay and coworkers. Accordingly, our continuum hydrodynamic model attributes a bulk viscosity reduction to a lower melt viscosity at the nanoparticle–polymer interface. Such a reduction has been ascribed to the Rouse dynamics of polymer chains at the nanoparticle–polymer interface. Fitting the theory to experimental data reveals a simple correlation between the reduced viscosity layer thickness, polymer chain size, entanglement tube diameter, and nanoparticle size and concentration. Our calculations support the arguments of Mackay and coworkers that nanoparticle inclusions significantly influence the polymer chain conformation in melts, even when the inclusion volume fraction is very small.

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.

Mass transfer from ensembles of fluid spheres to a power-law liquid at moderate Reynolds and Peclet numbers

The steady convective mass transfer from ensembles of mono-size Newtonian fluid spheres to power-law liquids has been studied at moderate Reynolds and Peclet numbers. The species continuity equation segregated from momentum equations has been solved numerically using a finite difference method. A simple cell model has been used to account for the modification of the flow field due to the neighbouring droplets. Extensive numerical results have been obtained which elucidate effects of the Reynolds number ( Re o ) , Schmidt number ( Sc), power-law index ( n o ) , internal to external fluid characteristic viscosity ratio ( k ) and the volume fraction of the dispersed phase ( Φ ) on the rate of mass transfer. The ranges of parameters considered herein are: 1 ⩽ Re o ⩽ 200 , 1 ⩽ Sc ⩽ 10000 , 0.6 ⩽ n o ⩽ 1.6 , 0.1 ⩽ k ⩽ 50 and 0.2 ⩽ Φ ⩽ 0.6 . For shear-thinning fluids ( n o < 1 ) , the rate of mass transfer is somewhat enhanced whereas for shear-thickening fluids ( n o > 1 ) , it decreased as compared to that in Newtonian fluids ( n o = 1 ) . A simple predictive correlation has been proposed which can be used to estimate the rate of mass transfer in liquid–liquid systems in a new application involving power-law continuous phase.

Drag on ensembles of fluid spheres translating in a power-law liquid at moderate Reynolds numbers

This work elucidates the role of power-law rheology on the sedimentation velocity of an ensemble of mono-size spherical Newtonian droplets (free from surfactants) translating in a power-law continuous phase numerically by solving the momentum equations of both phases. A simple sphere-in-sphere cell model has been used to account for inter-drop interactions. In particular, in this study, the effects of the Reynolds number (Reo), the internal to external fluid characteristic viscosity ratio (k), the volume fraction of the dispersed phase (Φ) and the power-law index of the continuous phase (no) on the external flow field, pressure drag (Cdp), friction drag (Cdf) and total drag (Cd) coefficients have been analyzed over wide ranges of parameters as follows: 1 ≤ Reo ≤ 200, 0.1 ≤ k ≤ 50, 0.2 ≤ Φ ≤ 0.6 and 0.6 ≤ no ≤ 1.6. Based on the extensive numerical results obtained in this work, a simple predictive correlation has been proposed for the total drag coefficient, which can be used to predict the rate of sedimentation of ensembles of Newtonian fluid spheres in power-law liquids in a new application.

Mass transfer from a single fluid sphere to power-law liquids at moderate Reynolds numbers

The steady-state convective inter-phase mass transfer from a single Newtonian fluid sphere (free from surfactants) to a continuous phase with power-law viscosity has been studied at moderate Reynolds and Schmidt numbers under the conditions when the resistance to mass transfer in the dispersed phase is negligible. The species continuity equation, segregated from the momentum equations of both phases, has been numerically solved using a finite difference method. The effects of the Reynolds number ( Re o ) , power-law index ( n o ) , internal to external fluid characteristic viscosity ratio ( k ) and Schmidt number ( Sc) on the local and average Sherwood number ( Sh) have been analysed over the following ranges of conditions: 5 ⩽ Re o ⩽ 200 , 0.6 ⩽ n o ⩽ 1.6 , 0.1 ⩽ k ⩽ 50 and 1 ⩽ Sc ⩽ 1000 . It has been observed that irrespective of the values of the Reynolds number and of the power-law index, as the value of k increases the average Sherwood number decreases for intermediate to large values of the Peclet number. As the value of the power-law index increases, the rate of mass transfer decreases for all values of the Reynolds number and the characteristic viscosity ratio thereby suggesting that shear-thinning behaviour facilitates mass transfer, whereas shear-thickening behaviour impedes it. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer of a fluid sphere sedimenting in power-law liquids.